Binomial Theorem一問

Coefficient of x^2 term in (1 + x)^n is n(n - 1)/2!
The x^2 term in (1 + 2x)^n is n(n - 1)/2![2x]^2, so the coefficient is 4n(n - 1)/2!
So n(n - 1)/2! + 4n(n - 1)/2! = 75
n^2 - n + 4n^2 - 4n = 150
5n^2 - 5n - 150 = 0
n^2 - n - 30 = 0
(n - 6)(n + 5) = 0
so n = 6 or - 5 (rej. since n is a positive integer).